# Is there a name for this type of plot? (function on complex plane vs time shown in 3D)

I'm just looking for a name for this type of plot, which is time vs real part vs imaginary part shown as a space curve.

Complex exponential:

Used to explain chirplets:

Complex Morlet wavelet shown this way:

instead of being shown as two plots:

the original 1998 source of which just calls them "complex analytical vibration signatures".

• I've seen the inverse of your situation, where a given space curve's projections on the coordinate planes are plotted along with the space curve itself, referred to as a "shadow plot". – J. M. isn't a mathematician May 12 '12 at 16:33
• Another example: pacifict.com/Examples/Gallery42.html "Complex functions of a real parameter A complex function of a real parameter can be drawn as a curve in 3D." – endolith Jun 30 '12 at 1:31
• Another example: ccrma.stanford.edu/~jos/st/… – endolith Jan 16 '13 at 2:50

A possible name is the Heyser corkscrew or the generalized Heyser spiral, at least for cisoids. It appears for instance in The Analytic Impulse, Andrew Duncan, JAES Volume 36 Issue 5 pp. 315-327; May 1988.

A complex analytic function is to its real part as a solid object is to its shadow. the analytic impulse $\Delta(t)$ is a complex "function" whose real part is the familiar Dirac symbol $\delta(t)$. This impulse finds application in energy-time calculations. The nature of this impulse and its application to finding energy-time curves are examined in the continuous, $z$-transform, and DFT domains. A simple window is also discussed which leads to a smoother impulse $\tilde{\Delta}(t)$

It seems fairly general:

In a Heyser corkscrew this magnitude appears as the radial distance of the central figure to the time

with a display of the Heyser corkscrew plot of asinc(t)

However, as asked in the SE.DSP question 3D wiggle plot for an analytic signal: Heyser corkscrew/spiral, I did not find a lot of authoritative traces so far.

• FYI, the time projection is a cochleoid, but you probably knew that. It is not in the cissoid family. – Cye Waldman Sep 12 '17 at 0:24
• There might be a misunderstanding: I use "cisoid" (one s) for the "complex exponential", and not "cissoid" (like the one from Diocles). Was that the reason of your comment (took me time to understand)? – Laurent Duval Oct 2 '17 at 17:07